V. Andreasen et Fb. Christiansen, SLOW COEVOLUTION OF A VIRAL PATHOGEN AND ITS DIPLOID HOST, Philosophical transactions-Royal Society of London. Biological sciences, 348(1325), 1995, pp. 341-354
We study a population exposed to a lethal infectious disease. Host res
ponse is carried at one locus with two alleles while the pathogen occu
rs in two variants. Based on an SI-type epidemic model we derive expli
cit equations for the dynamics of each genotype. By assuming small var
iations in both host and disease, we obtain a separation in time scale
s between epidemic and evolutionary processes. This allows us to descr
ibe explicitly the changes in host and disease gene frequencies. The r
esulting model has a rich behaviour including multiple stable states a
nd oscillations. However, in the oscillatory situation the model is de
generate excluding the possibility of limit cycles. We show that the d
egeneracy can only be removed by frequency dependent selection in the
pathogen, for example by including direct interaction of virus in a fr
ee-living stage. The qualitative conclusions extend to an SIR-type epi
demic model, where recovery with immunity from the disease is possible
.